Search: id:A143135
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%I A143135
%S A143135 1,2,11,100,1261,20342,399671,9256840,246907321,7452534122,251099460611,
%T A143135 9341422237420,380293239870181,16815919738248542,802553031266952431,
%U A143135 41117164304824602640,2250747364089063475441
%N A143135 E.g.f. satisfies: A(x) = sin(x + A(x)^2) with A(0)=0.
%C A143135 Radius of convergence of A(x) is r = Pi/4 - 1/2, with A(r) = sqrt(2)/
               2.
%F A143135 E.g.f.: A(x) = sin(G(x)) where G(x) = x + A(x)^2 is the e.g.f. of A143134.
%F A143135 E.g.f. derivative: A'(x) = sqrt(1 - A(x)^2)/(1 - 2*A(x)*sqrt(1 - A(x)^2)).
%e A143135 A(x) = x + 2*x^2/2! + 11*x^3/3! + 100*x^4/4! + 1261*x^5/5! +...
%e A143135 A(x) = sin(G(x)) where G(x) = x + A(x)^2 is the e.g.f. of A143134:
%e A143135 G(x) = x + 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +...
%o A143135 (PARI) {a(n)=local(A=x);for(i=0,n,A=x + sin(A)^2);n!*polcoeff(sin(A),
               n)}
%o A143135 (PARI) {a(n)=n!*polcoeff(sin(serreverse(x-sin(x+x*O(x^n))^2)),n)}
%Y A143135 Cf. A143134, A143137.
%Y A143135 Sequence in context: A020559 A003579 A099169 this_sequence A056732 A157715 
               A001271
%Y A143135 Adjacent sequences: A143132 A143133 A143134 this_sequence A143136 A143137 
               A143138
%K A143135 nonn
%O A143135 1,2
%A A143135 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2008

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